ON THE GRAPH COLORING POLYTOPE

The graph coloring problem consists in assigning colors to the vertices of a given graph G such that no two adjacent vertices receive the same color and the number of used colors is as small as possible. In this paper, we investigate the graph coloring polytope P(G) defined as the convex hull of feasible solutions to the binary programming formulation of the problem. We remark that P(G) coincides with the stable set polytope of a graph constructed from the complement G of G. We derive facet-defining inequalities for P(G) from independent sets, odd holes, odd anti-holes and odd wheels in G.